Definition:Identity (Abstract Algebra)/Right Identity

Definition

Let $\struct {S, \circ}$ be an algebraic structure.

An element $e_R \in S$ is called a right identity (element) if and only if:

$\forall x \in S: x \circ e_R = x$

Also known as

A right identity is also known as:

• a right neutral element
• a right unit (particularly in the context of the ring product of a ring).

Also see

• Definition:Left Identity
• Definition:Identity Element

• Results about identity elements can be found here.

Sources

• 1964: W.E. Deskins: Abstract Algebra ... (previous) ... (next): Exercise $1.4: \ 9$
• 1965: J.A. Green: Sets and Groups ... (previous) ... (next): Chapter $4$. Groups: Exercise $5$
• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 4$: Neutral Elements and Inverses: Exercise $4.3$
• 1966: Richard A. Dean: Elements of Abstract Algebra ... (previous) ... (next): $\S 1.2$
• 1968: Ian D. Macdonald: The Theory of Groups ... (previous) ... (next): $\S 1$: Some examples of groups
• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 2$: Sets and functions: Operations
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $5$: Semigroups: Exercise $3$